When leaving then reconnecting a singleplayer world whilst riding a horse (or donkey or mule), you will spawn riding the horse with another identical horse with the same everything. It seems as if you take one horse with you when you leave, but it also fails to fully despawn, and so duplicates.
Duplicate of MC-13737, please use the search function to see if your bug has already been submitted. Currently over 55% of tickets are being closed as duplicate.